A Chapman-Enskog formalism for inertial suspensions

Physica A: Statistical Mechanics and its Applications

Volumn 334, Issue 3-4, 2004, Pages 385-416

  Subramanian, G ^a   Brady, J F ^a,b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

Chapman Enskog; Fokker Planck; Hydrodynamic interactions; Multiple scales; Smoluchowski

Indexed keywords

BROWNIAN MOVEMENT; HYDRODYNAMICS; MICROSTRUCTURE; PERTURBATION TECHNIQUES; POLYNOMIALS; PROBABILITY DENSITY FUNCTION; RHEOLOGY; STATISTICAL METHODS;

CHAPMAN-ENSKOG; FOKKER-PLANCK; HYDRODYNAMIC INTERACTION; MULTIPLE SCALES; SMOLUCHOWSKI;

SUSPENSIONS (FLUIDS);

EID: 0742268387     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2003.10.054     Document Type: Article

References (29)

1. Chandrasekhar S. Stochastic problems in physics and astronomy. Wax Nelson Selected Papers on Noise and Stochastic Processes. 1954;3-91 Dover, New York.
2. Smoluchowski M.V. Über brownsche Molekularbewegung unter Einwirkung äubere Kräfte und deren Susammenhang mit der verallgemeinerte Diffusionsgleichung. Ann. d. Physik. 48:1915;1103-1112.
3. Happel J., Brenner H. Low Reynolds Number Hydrodynamics, with Special Applications to Particulate Media. 1965;Prentice-Hall, Englewood Cliffs, NJ.
4. Brady J.F., Bossis G. Stokesian dynamics. Ann. Rev. Fluid Mech. 20:1988;111-157.
5. Kim S., Karrila S.J. Microhydrodynamics: Principles and Applications. 1991;Butterworth-Heinemann, London.
6. Jenkins J.T., Savage S.B. A theory for the rapid flow of identical, smooth, nearly elastic, spherical-particles. J. Fluid Mech. 130:1983;187-202.
7. Lun C.K.K., Savage S.B., Jeffrey D.J. Kinetic theories for granular flow - inelastic particles in Couette-flow and slightly inelastic particles in a general flowfield. J. Fluid Mech. 140:1984;223-256.
8. Jenkins J.T., Richman M.W. Grads 13-moment system for a dense gas of inelastic spheres. Arch. Rational Mech. Anal. 87(4):1985;355-377.
9. Jenkins J.T., Richman M.W. Kinetic-theory for plane flows of a dense gas of identical, rough, inelastic, circular disks. Phys. Fluids. 28(12):1985;3485-3494.
10. Campbell C.S. Rapid granular flows. Ann. Rev. Fluid Mech. 22:1990;57-92.
11. Sangani A.S., Mo G., Tsao H.K., Koch D.L. Simple shear flow of dense gas-solid suspensions at finite Stokes numbers. J. Fluid Mech. 313:1996;309-341.
12. Tsao H.K., Koch D.L. Simple shear flows of dilute gas-solid suspensions. J. Fluid Mech. 296:1995;211-245.
13. 2) J. Fluid Mech. 56:1972;401-427.
14. Brady J.F., Morris J.F. Microstructure of strongly sheared suspensions and its impact on rheology and diffusion. J. Fluid Mech. 348:1997;103-139.
15. Chapman S., Cowling T.G. The Mathematical Theory of Non-uniform Gases. 1970;Cambridge University Press, Cambridge, MA.
16. Titulaer U.M. A systematic solution procedure for the Fokker-Planck equation of a Brownian particle in the high-friction case. Physica A. 91:1978;321-344.
17. Wycoff D., Balazs N.L. Multiple time scales analysis for the Kramers-Chandrasekhar equation. Physica A. 146:1987;175-200.
18. Yurkovetsky Y., Brady J.F. Statistical mechanics of bubbly liquids. Phys. Fluids. 8(4):1996;881-895.
19. Grassia P.S., Hinch E.J., Nitsche L.C. Computer simulations of Brownian motion of complex systems. J. Fluid Mech. 282:1995;373-403.
20. H. Risken, The Fokker-Planck Equation, Springer, Berlin, 1989, p. 25.
21. Santamaría-Holek I., Reguera D., Rubí J.M. Diffusion in stationary flow from mesoscopic nonequilibrium thermodynamics. Phys. Rev. E. 63:2001;051106.
22. Jeffrey D.J., Acrivos A. Rheological properties of suspensions of rigid particles. A.I.Ch.E. J. 22(3):1976;417-436.
23. Rallison J.M., Hinch E.J. The effect of particle interactions on dynamic light scattering from a dilute suspension. J. Fluid Mech. 167:1986;131-168.
24. Grad H. A note on. N -dimensional Hermite polynomials Comm. Pure Appl. Math. 2:1949;331.
25. Wycoff D., Balazs N.L. Multiple time scales analysis for the Kramers-Chandrasekhar equation with a weak magnetic field. Physica A. 146:1987;201-218.
26. G. Subramanian, Inertial effects in suspension dynamics, Ph.D. Thesis, California Institute of Technology, Pasadena, USA, 2002.
27. G. Subramanian, J.F. Brady, Trajectory analysis for non-Brownian inertial suspensions in simple shear flow I-trajectories in the shearing plane, Journal of Fluid Mechanics (submitted for review).
28. Cercignani C. Theory and Application of the Boltzmann Equation. 1975;Elsevier, Amsterdam.
29. G. Subramanian, J.F. Brady, Multiple scales analysis of the Fokker-Planck equation for simple shear flow, Physica A (2003) doi: 10.1016/j.physa.2003.10.055 (referred to as (I) in the text).